Method for calculating productivity of highly-deviated well suitable for ultra-low permeability reservoir

Abstract

The invention provides a highly-deviated well productivity calculation method suitable for an ultra-low permeability reservoir, which comprises the following steps: step 1) aiming at the ultra-low permeability reservoir, considering a seepage velocity v with a starting pressure gradient; 2) considering the stress sensitivity of the ultra-low permeability reservoir to obtain the average permeability; 3) obtaining the predicted productivity of the single crack according to the seepage velocity and the average permeability integral; (4) well deviation, fracturing cracks and well circumference radial conflux effect skin are considered respectively, the predicted productivity of the single crack is corrected, and the yield of the single crack of the highly-deviated well with various factors comprehensively considered is obtained; and (5) adding the yields of all the single cracks to obtain the whole well yield of the highly-deviated well. According to the method, on the basis of the oil reservoir seepage mechanics theory, the specific starting pressure gradient and stress sensitivity of the ultra-low permeability oil reservoir are considered, the comprehensive well deviation, fracturing cracks and other factors are considered, the productivity evaluation method is established, and accurate calculation of the productivity of the highly-deviated well of the ultra-low permeability oil reservoir can be achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of oil well productivity calculation, and in particular relates to a method for calculating the productivity of a highly deviated well suitable for an ultra-low permeability oil reservoir. Background Art

[0002] Oil well productivity is one of the core indicators of oilfield development and an important basis for formulating reasonable technical policies for oilfield development and evaluating the effects of productivity construction. Oil well productivity is affected by many factors such as crude oil physical properties, reservoir properties, well inclination angle, completion conditions, etc., and the calculation method needs to be optimized in real time according to actual needs. At present, ultra-low permeability reservoirs are an important area of ​​oil exploration and development in my country, and the use of staged fracturing and high-angle wells is an effective means to increase the oil leakage area of ​​ultra-low permeability reservoirs and improve the degree of utilization. Therefore, it is urgent to further clarify the seepage mechanism of high-angle wells in ultra-low permeability reservoirs and optimize the productivity evaluation method of high-angle wells, which is of great significance to improving the development level of ultra-low permeability reservoirs.

[0003] Ultra-low permeability reservoirs all require fracturing to obtain effective production capacity. In the formation, the conductivity of the hydraulic fracture is much greater than that of the matrix, and it is the main seepage channel in the near-wellbore area. The fluid flowing from the matrix to the bottom of the well is usually negligible relative to the fracture. Therefore, after determining the production capacity of each fracture, the oil well production capacity can be equivalent to the sum of the production capacities of each hydraulic fracture.

[0004] In the process of oilfield development plan preparation, reservoir dynamic analysis and development technology policy optimization, as the requirements for economic benefit indicators become more and more stringent, accurately determining the oil well production capacity is the basis for formulating various plans and ensuring good benefits. A model that can truly reflect the seepage process of high-angle wells in ultra-low permeability reservoirs is particularly critical.

[0005] Based on the instantaneous function method, potential superposition theory, infinitesimal line convergence principle and mirror reflection principle, a high-angle well reservoir seepage model and wellbore flow model are established, and the models are coupled and solved to quantitatively analyze the impact of different sensitive parameters on the productivity of high-angle wells. However, this scheme does not consider the start-up pressure gradient and stress sensitivity of ultra-low permeability reservoirs, nor does it consider that hydraulic fractures are the main channels for seepage in the near-wellbore area.

[0006] Considering the quasi-steady-state production capacity of low-speed non-Darcy inclined wells under reservoir damage, through the study of the seepage characteristics of low-permeability reservoirs, while considering factors such as the start-up pressure gradient and reservoir damage, the dimensionless inflow dynamic equation of low-speed non-Darcy seepage in high-angle wells under quasi-stable seepage conditions is established. This scheme takes into account the particularity of ultra-low permeability reservoirs, but does not consider the impact of hydraulic fracturing.

[0007] CN201910122327.9 A method for calculating the productivity of highly deviated wells in low-permeability reservoirs, comprising: obtaining basic parameters; substituting the obtained basic parameters into the following formula to calculate the productivity of highly deviated wells in low-permeability reservoirs: where Q is the predicted productivity of the highly deviated well, μ0 is the viscosity of crude oil, hs is the length of the highly deviated well in the production interval, K is the absolute permeability of the oil reservoir, G r is the starting pressure gradient, r e is the oil supply radius, r w is the wellbore radius, S p is the pseudo-skin factor generated by the well deviation, S t is the true skin factor generated by reservoir damage, P e is the supply pressure, P wf is the bottom-hole pressure of the production well. This method addresses the problem of lacking relevant parameters in predicting productivity using existing formulas, and proposes a new method for quickly calculating the productivity of highly deviated wells. Through this new calculation method, the productivity of highly deviated wells in low-permeability reservoirs can be calculated more accurately. Although this method considers the starting pressure gradient and has a certain applicability to low-permeability and unfractured reservoirs, it does not consider the stress sensitivity of low-permeability reservoirs and the decisive influence of fracture on the productivity of highly deviated wells, resulting in inaccurate calculation of the productivity of highly deviated wells in ultra-low-permeability reservoirs. Summary of the Invention

[0008] The purpose of the present invention is to provide a method for calculating the productivity of highly deviated wells applicable to ultra-low-permeability reservoirs. Based on the theory of reservoir seepage mechanics, considering the unique starting pressure gradient and stress sensitivity of ultra-low-permeability reservoirs, and integrating factors such as well deviation and fracture, a productivity calculation method is established. The present invention can accurately calculate the productivity of highly deviated wells in ultra-low-permeability reservoirs.

[0009] To this end, the technical solution provided by the present invention is as follows:

[0010] A method for calculating the productivity of highly deviated wells applicable to ultra-low-permeability reservoirs, comprising the following steps:

[0011] Step 1) For ultra-low-permeability reservoirs, consider the seepage velocity ν with a starting pressure gradient;

[0012] Step 2) Consider the stress sensitivity of ultra-low-permeability reservoirs to obtain the average permeability;

[0013] Step 3) Integrate the seepage velocity and average permeability to obtain the predicted productivity of a single fracture;

[0014] Step 4) Consider the well deviation, fracture, and skin effect of radial convergence around the wellbore respectively to correct the predicted productivity of a single fracture, and obtain the production of a single fracture of a highly deviated well considering various factors comprehensively;

[0015] Step 5) Add the production of each single fracture to obtain the total well production of the highly deviated well.

[0016] The seepage velocity ν in Step 1) is as follows:

[0017]

[0018] In the formula, K is the average reservoir permeability; μ0 is the crude oil viscosity under formation conditions; λ is the starting pressure gradient; p is the pressure; r is the radius.

[0019] The average permeability in Step 2) is obtained by the following formula:

[0020] K = K O exp[-α k (p e -p w )]

[0021] In the formula, K O is the original matrix permeability, p e is the supply pressure, p w is the bottom-hole pressure of the oil-producing well, α K is the stress sensitivity coefficient.

[0022] The predicted productivity q of a single fracture obtained in Step 3) i is as follows:

[0023]

[0024] In the formula, h is the length of the fracture in the production interval, r e is the drainage radius, r w is the wellbore radius, B o is the formation volume factor of the crude oil, p e is the supply pressure, p w is the bottom-hole pressure of the oil-producing well, α K is the stress sensitivity coefficient, λ is the starting pressure gradient, i is the number of fractures, i = 1, 2, 3,......, n.

[0025] The production q of a single fracture of the highly deviated well considering various factors in Step 4) i is calculated according to the following formula:

[0026]

[0027] In the formula, S θ is the skin factor caused by the well deviation, S f is the skin of the finite conductivity fracture, S C is the radial convergence skin; h i is the length of a certain fracture in the production interval; r e is the drainage radius, rw is the wellbore radius, B o is the formation volume factor of crude oil, p e is the supply pressure, p w is the bottom-hole pressure of the oil-producing well, α K is the stress sensitivity coefficient, λ is the starting pressure gradient, and i is the number of fractures.

[0028] The starting pressure gradient λ = 0.0091K -1.1994 .

[0029] The stress sensitivity coefficient α K is negatively correlated with the matrix permeability and is determined by the following relationship

[0030] α k = 0.1531K O -0.343

[0031] where K O is the original matrix permeability.

[0032] The skin factor S caused by well deviation θ is obtained by the following formula:

[0033]

[0034] where θ is the well deviation angle in the highly deviated section; h D is the vertical thickness of the oil layer; r w is the wellbore radius.

[0035] The skin factor S of the finite conductivity fracture f is obtained by the following formula:

[0036]

[0037] σ = ln(C fD )

[0038] where σ is the viscosity of crude oil; x f is the half-length of the fracture; C fD is the fracture conductivity; r w is the wellbore radius.

[0039] The skin factor S of the radial convergence C is obtained by the following formula:

[0040]

[0041] where K f is the fracture permeability; ω f is the fracture width.

[0042] The beneficial effects of the present invention are:

[0043] The productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs provided by the present invention combines the seepage physical characteristics of ultra-low permeability reservoirs and the completion and transformation methods of highly deviated wells, comprehensively considers factors such as well inclination, starting pressure gradient, stress sensitivity, and fracture pressure, and equates the total production of highly deviated wells to the sum of the production of each fracture. A productivity model for highly deviated wells with multi-cluster perforating and fracturing in ultra-low permeability reservoirs is established, improving the rationality and accuracy of productivity prediction for highly deviated wells. The established productivity model for highly deviated wells is compared and verified with the actual single-well liquid production data in the Huanqing block of Yumen Oilfield. The results show that the newly established productivity model considering various factors can calculate the productivity of highly deviated wells more accurately and can be used for predicting and analyzing the liquid production of highly deviated wells. Detailed implementation mode

[0044] The following specific embodiments illustrate the implementation mode of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification.

[0045] The exemplary implementation modes of the present invention are introduced below. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. These embodiments are provided to disclose the present invention in detail and completely and to fully convey the scope of the present invention to those skilled in the relevant technical field. The terms used in the exemplary implementation modes are not limitations on the present invention.

[0046] Unless otherwise specified, the terms (including scientific and technical terms) used herein have the ordinary meaning understood by those skilled in the relevant technical field. In addition, it can be understood that the terms defined in the commonly used dictionary should be understood to have a meaning consistent with the context of their relevant fields and should not be understood as idealized or overly formal meanings.

[0047] Embodiment 1

[0048] The present invention provides a productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs, including the following steps:

[0049] Step 1) For ultra-low permeability reservoirs, consider the seepage velocity ν with a starting pressure gradient.

[0050] Step 2) Consider the stress sensitivity of ultra-low permeability reservoirs to obtain the average permeability.

[0051] Step 3) Integrate according to the seepage velocity and average permeability to obtain the predicted productivity of a single fracture.

[0052] Step 4) Consider the well inclination, fracture pressure, and skin effect of radial convergence around the well respectively to correct the predicted productivity of a single fracture, and obtain the production of a single fracture of a highly deviated well considering various factors.

[0053] Step 5) Add the production of each single fracture to obtain the total well production of the highly deviated well.

[0054] Based on the reservoir seepage mechanics theory, considering the unique starting pressure gradient and stress sensitivity of the ultra-low permeability reservoir, and integrating factors such as well deviation and fracture, the present invention establishes a productivity calculation method, which can accurately calculate the productivity of highly deviated wells in ultra-low permeability reservoirs.

[0055] Example 2

[0056] On the basis of Example 1, the present invention provides a productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs, including the following steps:

[0057] Step 1) For an ultra-low permeability reservoir, consider the seepage velocity ν with a starting pressure gradient.

[0058]

[0059] In the formula, K is the average permeability of the reservoir; μ0 is the viscosity of crude oil under formation conditions; λ is the starting pressure gradient; p is the pressure; r is the radius; λ is the starting pressure gradient, which can be determined by the following relational expression: λ = 0.0091K -1.1994 .

[0060] Step 2) Considering the stress sensitivity of the ultra-low permeability reservoir, obtain the average permeability K.

[0061] K = K O exp[-α k (p e -p w )]

[0062] In the formula, p e is the supply pressure, p w is the bottom-hole pressure of the oil production well, and α K is the stress sensitivity coefficient, which is negatively correlated with the matrix permeability and can be determined by the following relational expression:

[0063] α k = 0.1531K O -0.343

[0064] In the formula, K O is the original matrix permeability.

[0065] Step 3) Integrate according to the seepage velocity and the average permeability to obtain the predicted productivity of a single fracture; that is, substitute the average permeability relational expression into the seepage velocity ν relational expression, and after integration, obtain the predicted productivity q of a single fracture i as the following formula:

[0066]

[0067] In the formula, h is the length of the fracture in the production interval, r e is the drainage radius, r w is the wellbore radius, B o is the formation volume factor of crude oil, p e is the supply pressure, p w is the bottom-hole pressure of the oil-producing well, α K is the stress sensitivity coefficient, λ is the starting pressure gradient, i is the number of fractures, and i = 1, 2, 3,......, n.

[0068] Step 4) Consider the well deviation, fracture with finite conductivity, and skin effect of radial flow around the wellbore respectively, and correct the single-fracture predicted productivity in Step 3) to obtain the single-fracture production of the highly deviated well considering various factors;

[0069]

[0070] In the formula, S θ is the skin factor caused by well deviation, S f is the skin of the fracture with finite conductivity, S C is the skin of radial flow; h i is the length of a certain fracture in the production interval.

[0071] The skin factor S caused by well deviation θ is obtained by the following formula:

[0072]

[0073] In the formula, θ is the well deviation angle in the highly deviated section; h D is the vertical thickness of the oil reservoir; r w is the wellbore radius.

[0074] The skin S of the fracture with finite conductivity f is obtained by the following formula:

[0075]

[0076] σ = ln(C fD )

[0077] In the formula, σ is the viscosity of crude oil; x f is the half-length of the fracture; C fD is the fracture conductivity.

[0078] The skin S of radial flow C is obtained by the following formula:

[0079]

[0080] In the formula, K f is the fracture permeability; ω fis the crack width.

[0081] Step 5) The total well production of the highly deviated well can be regarded as the sum of the production of each hydraulic fracture, i.e.:

[0082]

[0083] Example 3

[0084] To further illustrate the effect of the present invention, this example takes Well Q, a highly deviated well in the Chang 8 formation in the eastern part of the Huanqing block, as an example.

[0085] This well is located in a certain well area in the eastern Chang 8 formation. The supply pressure p e = 19.9 MPa, the bottom hole pressure p w = 9 MPa, the oil supply radius r e = 350 m, the wellbore radius r w = 0.1 m, the crude oil viscosity σ = 1.3 mPa·S, the crude oil volume factor B o = 1.37, the reservoir matrix permeability K f = 0.51×10 -3 μm 2 , the vertical thickness h of the oil layer drilled through D = 13.3 m, the well deviation angle θ = 68°, including 6 hydraulic fractures, the half-length x of the hydraulic fracture f = 100 m, the fracture width ω f = 0.01 m, the fracture conductivity C fD takes the value of 1.6. After the liquid drainage period of this well ends, the stable liquid production is 9 m 3 / d.

[0086] Calculate the productivity of 6 hydraulic fractures respectively, and the theoretical liquid production of Well Q is 8.4 m 3 / d after summation, and the relative error compared with the actual liquid production is only 0.07.

[0087] Use the current two common models to calculate the productivity of Well Q respectively. Model 1 (the literature "Productivity Prediction Method for (Pseudo) Steady Flow Inclined Straight Wells") only considers the well deviation skin effect and calculates the liquid production of 1.6 m 3 / d, with a relative error of 0.82, which is the largest; Model 2 (CN201910122327.9, a method for calculating the productivity of highly deviated wells in low-permeability oil reservoirs) calculates the liquid production of 6.8 m 3 / d, with a relative error of 0.24, and the error is relatively large.

[0088] In summary, compared with the solutions with relatively single consideration factors in the existing methods, the present invention establishes a calculation method that comprehensively considers factors such as well deviation, starting pressure gradient, stress sensitivity, and hydraulic fracture based on the theory of reservoir seepage mechanics, improving the rationality and accuracy of productivity prediction for highly deviated wells. The productivity model for highly deviated wells established is verified by comparing with the actual single-well liquid production data of the Huanqing block in the Yumen Oilfield. The results show that the newly established productivity model considering multiple factors can calculate the productivity of highly deviated wells more accurately and can be used for predicting and analyzing the liquid production of highly deviated wells.

[0089] The above examples are only illustrative of the present invention and do not constitute a limitation on the protection scope of the present invention. Any design identical or similar to the present invention falls within the protection scope of the present invention.

Claims

1. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs, characterized in that: Including the following steps: Step 1) For an ultra-low permeability reservoir, consider the seepage velocity ν with a starting pressure gradient; Step 2) Consider the stress sensitivity of the ultra-low permeability reservoir to obtain the average permeability; Step 3) Integrate according to the seepage velocity and the average permeability to obtain the predicted productivity of a single fracture; Step 4) Respectively consider the well deviation, the hydraulic fracture, and the skin effect of the radial convergence around the wellbore to correct the predicted productivity of a single fracture, and obtain the production of a single fracture in a highly deviated well considering various factors comprehensively; Step 5) Add the productions of each single fracture to obtain the total well production of the highly deviated well.

2. The productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 1, characterized in that: The seepage velocity ν in Step 1) is as follows: In the formula, K is the average permeability of the reservoir; μ0 is the viscosity of crude oil under formation conditions; λ is the starting pressure gradient; p is the pressure; r is the radius.

3. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 1, characterized in that: The average permeability in Step 2) is obtained through the following formula: K = K O exp[-α k (p e - p w )] Where K O is the original permeability of the matrix, p e is the supply pressure, p w is the bottom-hole pressure of the oil production well, and α K is the stress sensitivity coefficient.

4. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 1, characterized in that: The predicted production capacity q of a single crack obtained in step 3) i is given by the following formula: Where h is the length of the fracture in the production interval, r e is the drainage radius, r w is the wellbore radius, B o is the formation volume factor of crude oil, p e is the supply pressure, p w is the bottom-hole pressure of the oil-producing well, α K is the stress sensitivity coefficient, λ is the starting pressure gradient, i is the number of fractures, and i = 1, 2, 3,......, n.

5. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 1, characterized in that: The production q of a single fracture in a highly deviated well considering various factors in step 4 i is calculated according to the following formula: Wherein, S θ is the skin factor caused by well deviation, S f is the finite conductivity fracture skin, S C is the radial convergence skin; h i is the length of a certain fracture in the production interval; r e is the drainage radius, r w is the wellbore radius, B o is the oil formation volume factor, p e is the supply pressure, p w is the bottom-hole pressure of the oil production well, α K is the stress sensitivity coefficient, λ is the starting pressure gradient, and i is the number of fractures.

6. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 2, characterized in that: Starting pressure gradient λ = 0.0091K -1.1994 .

7. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 3, characterized in that: Stress sensitivity coefficient α K Is negatively correlated with the matrix permeability and is determined by the following relationship α k ＝0.1531K O -0.343 where K O is the original permeability of the matrix.

8. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 5, characterized in that: Skin factor S caused by well deviation θ Obtained by the following formula: In the formula, θ is the well deviation angle of the highly deviated section; h D is the vertical thickness of the oil reservoir; r w is the wellbore radius.

9. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 5, characterized in that: Finite conductivity fracture skin S f is obtained by the following formula: σ = ln(C fD ) where σ is the viscosity of crude oil; x f is the half-length of the fracture; C fD is the fracture conductivity; r w is the wellbore radius.

10. A productivity calculation method for highly deviated wells applicable to ultra-low permeability reservoirs according to claim 5, characterized in that: Radial flow-concentrating skin S C Obtained by the following formula: where K f is the fracture permeability; ω f is the fracture width.

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